Problem: What's the first wrong statement in the proof below that $ \triangle CEB \cong \triangle CEF$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle CEF \cong \angle BAC$ $, \ $ $ \overline{CE} \cong \overline{AC}$ $, \ $ $ \angle ECF \cong \angle ACB$ $, \ $ $ \overline{CF} \cong \overline{BD}$ $, \ $ $ \angle CFE \cong \angle DBE$ $, \ $ and $\ $ $ \angle CEF \cong \angle BED$ Proof $ \triangle CAB \cong \triangle CEF$ because ASA $ \overline{BC} \cong \overline{CF}$ because corresponding parts of congruent triangles are congruent $ \angle CBE \cong \angle ABC$ because corresponding parts of congruent triangles are congruent $ \angle CEF \cong \angle BCE$ because alternate interior angles are equal $ \triangle CEF \cong \triangle DEB$ because AAS $ \triangle CEB \cong \triangle CEF$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle ABC \cong \angle CBE$ is the first wrong statement.